Mike Davies

Dongdong Chen, Mike Davies, Matthias J. Ehrhardt et al.

From early image processing to modern computational imaging, successful models and algorithms have relied on a fundamental property of natural signals: symmetry. Here symmetry refers to the invariance property of signal sets to transformations such as translation, rotation or scaling. Symmetry can also be incorporated into deep neural networks in the form of equivariance, allowing for more data-efficient learning. While there has been important advances in the design of end-to-end equivariant networks for image classification in recent years, computational imaging introduces unique challenges for equivariant network solutions since we typically only observe the image through some noisy ill-conditioned forward operator that itself may not be equivariant. We review the emerging field of equivariant imaging and show how it can provide improved generalization and new imaging opportunities. Along the way we show the interplay between the acquisition physics and group actions and links to iterative reconstruction, blind compressed sensing and self-supervised learning.

Julián Tachella, Dongdong Chen, Mike Davies

Solving an ill-posed linear inverse problem requires knowledge about the underlying signal model. In many applications, this model is a priori unknown and has to be learned from data. However, it is impossible to learn the model using observations obtained via a single incomplete measurement operator, as there is no information about the signal model in the nullspace of the operator, resulting in a chicken-and-egg problem: to learn the model we need reconstructed signals, but to reconstruct the signals we need to know the model. Two ways to overcome this limitation are using multiple measurement operators or assuming that the signal model is invariant to a certain group action. In this paper, we present necessary and sufficient sensing conditions for learning the signal model from measurement data alone which only depend on the dimension of the model and the number of operators or properties of the group action that the model is invariant to. As our results are agnostic of the learning algorithm, they shed light into the fundamental limitations of learning from incomplete data and have implications in a wide range set of practical algorithms, such as dictionary learning, matrix completion and deep neural networks.

Jason Yik, Korneel Van den Berghe, Douwe den Blanken et al. · eth-zurich

Neuromorphic computing shows promise for advancing computing efficiency and capabilities of AI applications using brain-inspired principles. However, the neuromorphic research field currently lacks standardized benchmarks, making it difficult to accurately measure technological advancements, compare performance with conventional methods, and identify promising future research directions. Prior neuromorphic computing benchmark efforts have not seen widespread adoption due to a lack of inclusive, actionable, and iterative benchmark design and guidelines. To address these shortcomings, we present NeuroBench: a benchmark framework for neuromorphic computing algorithms and systems. NeuroBench is a collaboratively-designed effort from an open community of researchers across industry and academia, aiming to provide a representative structure for standardizing the evaluation of neuromorphic approaches. The NeuroBench framework introduces a common set of tools and systematic methodology for inclusive benchmark measurement, delivering an objective reference framework for quantifying neuromorphic approaches in both hardware-independent (algorithm track) and hardware-dependent (system track) settings. In this article, we outline tasks and guidelines for benchmarks across multiple application domains, and present initial performance baselines across neuromorphic and conventional approaches for both benchmark tracks. NeuroBench is intended to continually expand its benchmarks and features to foster and track the progress made by the research community.

Elvin Hajizada, Danielle Rager, Timothy Shea et al.

AI systems on edge devices face a critical challenge in open-world environments: adapting when data distributions shift and novel classes emerge. While offline training dominates current paradigms, online continual learning (OCL)--where models learn incrementally from non-stationary streams without catastrophic forgetting--remains challenging in power-constrained settings. We present a neuromorphic solution called CLP-SNN: a spiking neural network architecture for Continually Learning Prototypes and its implementation on Intel's Loihi 2 chip. Our approach introduces three innovations: (1) event-driven and spatiotemporally sparse local learning, (2) a self-normalizing three-factor learning rule maintaining weight normalization, and (3) integrated neurogenesis and metaplasticity for capacity expansion and forgetting mitigation. On OpenLORIS few-shot learning experiments, CLP-SNN achieves accuracy competitive with replay methods while being rehearsal-free. CLP-SNN delivers transformative efficiency gains: 70\times faster (0.33ms vs 23.2ms), and 5,600\times more energy efficient (0.05mJ vs 281mJ) than the best alternative OCL on edge GPU. This demonstrates that co-designed brain-inspired algorithms and neuromorphic hardware can break traditional accuracy-efficiency trade-offs for future edge AI systems.

Julián Tachella, Mike Davies, Laurent Jacques

Recently, many self-supervised learning methods for image reconstruction have been proposed that can learn from noisy data alone, bypassing the need for ground-truth references. Most existing methods cluster around two classes: i) Stein's Unbiased Risk Estimate (SURE) and similar approaches that assume full knowledge of the noise distribution, and ii) Noise2Self and similar cross-validation methods that require very mild knowledge about the noise distribution. The first class of methods tends to be impractical, as the noise level is often unknown in real-world applications, and the second class is often suboptimal compared to supervised learning. In this paper, we provide a theoretical framework that characterizes this expressivity-robustness trade-off and propose a new approach based on SURE, but unlike the standard SURE, does not require knowledge about the noise level. Throughout a series of experiments, we show that the proposed estimator outperforms other existing self-supervised methods on various imaging inverse problems.

Lyes Khacef, Philipp Weidel, Susumu Hogyoku et al.

Fall detection for elderly care using non-invasive vision-based systems remains an important yet unsolved problem. Driven by strict privacy requirements, inference must run at the edge of the vision sensor, demanding robust, real-time, and always-on perception under tight hardware constraints. To address these challenges, we propose a neuromorphic fall detection system that integrates the Sony IMX636 event-based vision sensor with the Intel Loihi 2 neuromorphic processor via a dedicated FPGA-based interface, leveraging the sparsity of event data together with near-memory asynchronous processing. Using a newly recorded dataset under diverse environmental conditions, we explore the design space of sparse neural networks deployable on a single Loihi 2 chip and analyze the tradeoffs between detection F1 score and computational cost. Notably, on the Pareto front, our LIF-based convolutional SNN with graded spikes achieves the highest computational efficiency, reaching a 55x synaptic operations sparsity for an F1 score of 58%. The LIF with graded spikes shows a gain of 6% in F1 score with 5x less operations compared to binary spikes. Furthermore, our MCUNet feature extractor with patched inference, combined with the S4D state space model, achieves the highest F1 score of 84% with a synaptic operations sparsity of 2x and a total power consumption of 90 mW on Loihi 2. Overall, our smart security camera proof-of-concept highlights the potential of integrating neuromorphic sensing and processing for edge AI applications where latency, energy consumption, and privacy are critical.

Andrew Wang, Mike Davies

Reconstructing dynamic MRI image sequences from undersampled accelerated measurements is crucial for faster and higher spatiotemporal resolution real-time imaging of cardiac motion, free breathing motion and many other applications. Classical paradigms, such as gated cine MRI, assume periodicity, disallowing imaging of true motion. Supervised deep learning methods are fundamentally flawed as, in dynamic imaging, ground truth fully-sampled videos are impossible to truly obtain. We propose an unsupervised framework to learn to reconstruct dynamic MRI sequences from undersampled measurements alone by leveraging natural geometric spatiotemporal equivariances of MRI. Dynamic Diffeomorphic Equivariant Imaging (DDEI) significantly outperforms state-of-the-art unsupervised methods such as SSDU on highly accelerated dynamic cardiac imaging. Our method is agnostic to the underlying neural network architecture and can be used to adapt the latest models and post-processing approaches. Our code and video demos are at https://github.com/Andrewwango/ddei.

Andrew Wang, Steven McDonagh, Mike Davies

Reconstructing MRI from highly undersampled measurements is crucial for accelerating medical imaging, but is challenging due to the ill-posedness of the inverse problem. While supervised deep learning (DL) approaches have shown remarkable success, they traditionally rely on fully-sampled ground truth (GT) images, which are expensive or impossible to obtain in real scenarios. This problem has created a recent surge in interest in self-supervised learning methods that do not require GT. Although recent methods are now fast approaching "oracle" supervised performance, the lack of systematic comparison and standard experimental setups are hindering targeted methodological research and precluding widespread trustworthy industry adoption. We present SSIBench, a modular and flexible comparison framework to unify and thoroughly benchmark Self-Supervised Imaging methods (SSI) without GT. We evaluate 18 methods across 4 realistic MRI scenarios on real data, showing a wide performance landscape whose method ranking differs across scenarios and metrics, exposing the need for further SSI research. Our insights also show how complementary methods could be compounded for future improvements, exemplified by a novel loss we propose, Multi-Operator Equivariant Imaging. To accelerate reproducible research and lower the barrier to entry, we provide the extensible benchmark and open-source reimplementations of all methods at https://andrewwango.github.io/ssibench, allowing researchers to rapidly and fairly contribute and evaluate new methods on the standardised setup for potential leaderboard ranking, or benchmark existing methods on custom datasets, forward operators, or models, unlocking the application of SSI to other valuable GT free domains such as 4D MRI and other nascent scientific imaging modalities.

Jiangwei Xie, Zhang Wen, Mike Davies et al.

Hyperspectral image (HSI) restoration is a fundamental challenge in computational imaging and computer vision. It involves ill-posed inverse problems, such as inpainting and super-resolution. Although deep learning methods have transformed the field through data-driven learning, their effectiveness hinges on access to meticulously curated ground-truth datasets. This fundamentally restricts their applicability in real-world scenarios where such data is unavailable. This paper presents SHARE (Single Hyperspectral Image Restoration with Equivariance), a fully unsupervised framework that unifies geometric equivariance principles with low-rank spectral modelling to eliminate the need for ground truth. SHARE's core concept is to exploit the intrinsic invariance of hyperspectral structures under differentiable geometric transformations (e.g. rotations and scaling) to derive self-supervision signals through equivariance consistency constraints. Our novel Dynamic Adaptive Spectral Attention (DASA) module further enhances this paradigm shift by explicitly encoding the global low-rank property of HSI and adaptively refining local spectral-spatial correlations through learnable attention mechanisms. Extensive experiments on HSI inpainting and super-resolution tasks demonstrate the effectiveness of SHARE. Our method outperforms many state-of-the-art unsupervised approaches and achieves performance comparable to that of supervised methods. We hope that our approach will shed new light on HSI restoration and broader scientific imaging scenarios. The code will be released at https://github.com/xuwayyy/SHARE.

Andrew Wang, Mike Davies

Ill-posed image reconstruction problems appear in many scenarios such as remote sensing, where obtaining high quality images is crucial for environmental monitoring, disaster management and urban planning. Deep learning has seen great success in overcoming the limitations of traditional methods. However, these inverse problems rarely come with ground truth data, highlighting the importance of unsupervised learning from partial and noisy measurements alone. We propose perspective-equivariant imaging (EI), a framework that leverages classical projective camera geometry in optical imaging systems, such as satellites or handheld cameras, to recover information lost in ill-posed camera imaging problems. We show that our much richer non-linear class of group transforms, derived from camera geometry, generalises previous EI work and is an excellent prior for satellite and urban image data. Perspective-EI achieves state-of-the-art results in multispectral pansharpening, outperforming other unsupervised methods in the literature. Code at https://github.com/Andrewwango/perspective-equivariant-imaging.

Andrew Wang, Mike Davies

Multispectral demosaicing is crucial to reconstruct full-resolution spectral images from snapshot mosaiced measurements, enabling real-time imaging from neurosurgery to autonomous driving. Classical methods are blurry, while supervised learning requires costly ground truth (GT) obtained from slow line-scanning systems. We propose Perspective-Equivariant Fine-tuning for Demosaicing (PEFD), a framework that learns multispectral demosaicing from mosaiced measurements alone. PEFD a) exploits the projective geometry of camera-based imaging systems to leverage a richer group structure than previous demosaicing methods to recover more null-space information, and b) learns efficiently without GT by adapting pretrained foundation models designed for 1-3 channel imaging. On intraoperative and automotive datasets, PEFD recovers fine details such as blood vessels and preserves spectral fidelity, substantially outperforming recent approaches, nearing supervised performance.

Jérémy Scanvic, Mike Davies, Patrice Abry et al.

Self-supervised methods have recently proved to be nearly as effective as supervised ones in various imaging inverse problems, paving the way for learning-based approaches in scientific and medical imaging applications where ground truth data is hard or expensive to obtain. These methods critically rely on invariance to translations and/or rotations of the image distribution to learn from incomplete measurement data alone. However, existing approaches fail to obtain competitive performances in the problems of image super-resolution and deblurring, which play a key role in most imaging systems. In this work, we show that invariance to roto-translations is insufficient to learn from measurements that only contain low-frequency information. Instead, we propose scale-equivariant imaging, a new self-supervised approach that leverages the fact that many image distributions are approximately scale-invariant, enabling the recovery of high-frequency information lost in the measurement process. We demonstrate throughout a series of experiments on real datasets that the proposed method outperforms other self-supervised approaches, and obtains performances on par with fully supervised learning.

Shuo Li, Mike Davies, Mehrdad Yaghoobi

Hyperspectral imaging (HSI) is a key technology for earth observation, surveillance, medical imaging and diagnostics, astronomy and space exploration. The conventional technology for HSI in remote sensing applications is based on the push-broom scanning approach in which the camera records the spectral image of a stripe of the scene at a time, while the image is generated by the aggregation of measurements through time. In real-world airborne and spaceborne HSI instruments, some empty stripes would appear at certain locations, because platforms do not always maintain a constant programmed attitude, or have access to accurate digital elevation maps (DEM), and the travelling track is not necessarily aligned with the hyperspectral cameras at all times. This makes the enhancement of the acquired HS images from incomplete or corrupted observations an essential task. We introduce a novel HSI inpainting algorithm here, called Hyperspectral Equivariant Imaging (Hyper-EI). Hyper-EI is a self-supervised learning-based method which does not require training on extensive datasets or access to a pre-trained model. Experimental results show that the proposed method achieves state-of-the-art inpainting performance compared to the existing methods.

Julián Tachella, Dongdong Chen, Mike Davies

In many real-world inverse problems, only incomplete measurement data are available for training which can pose a problem for learning a reconstruction function. Indeed, unsupervised learning using a fixed incomplete measurement process is impossible in general, as there is no information in the nullspace of the measurement operator. This limitation can be overcome by using measurements from multiple operators. While this idea has been successfully applied in various applications, a precise characterization of the conditions for learning is still lacking. In this paper, we fill this gap by presenting necessary and sufficient conditions for learning the underlying signal model needed for reconstruction which indicate the interplay between the number of distinct measurement operators, the number of measurements per operator, the dimension of the model and the dimension of the signals. Furthermore, we propose a novel and conceptually simple unsupervised learning loss which only requires access to incomplete measurement data and achieves a performance on par with supervised learning when the sufficient condition is verified. We validate our theoretical bounds and demonstrate the advantages of the proposed unsupervised loss compared to previous methods via a series of experiments on various imaging inverse problems, such as accelerated magnetic resonance imaging, compressed sensing and image inpainting.

Garrick Orchard, E. Paxon Frady, Daniel Ben Dayan Rubin et al.

The biologically inspired spiking neurons used in neuromorphic computing are nonlinear filters with dynamic state variables -- very different from the stateless neuron models used in deep learning. The next version of Intel's neuromorphic research processor, Loihi 2, supports a wide range of stateful spiking neuron models with fully programmable dynamics. Here we showcase advanced spiking neuron models that can be used to efficiently process streaming data in simulation experiments on emulated Loihi 2 hardware. In one example, Resonate-and-Fire (RF) neurons are used to compute the Short Time Fourier Transform (STFT) with similar computational complexity but 47x less output bandwidth than the conventional STFT. In another example, we describe an algorithm for optical flow estimation using spatiotemporal RF neurons that requires over 90x fewer operations than a conventional DNN-based solution. We also demonstrate promising preliminary results using backpropagation to train RF neurons for audio classification tasks. Finally, we show that a cascade of Hopf resonators - a variant of the RF neuron - replicates novel properties of the cochlea and motivates an efficient spike-based spectrogram encoder.

Denis Kleyko, Mike Davies, E. Paxon Frady et al.

This article reviews recent progress in the development of the computing framework vector symbolic architectures (VSA) (also known as hyperdimensional computing). This framework is well suited for implementation in stochastic, emerging hardware, and it naturally expresses the types of cognitive operations required for artificial intelligence (AI). We demonstrate in this article that the field-like algebraic structure of VSA offers simple but powerful operations on high-dimensional vectors that can support all data structures and manipulations relevant to modern computing. In addition, we illustrate the distinguishing feature of VSA, "computing in superposition," which sets it apart from conventional computing. It also opens the door to efficient solutions to the difficult combinatorial search problems inherent in AI applications. We sketch ways of demonstrating that VSA are computationally universal. We see them acting as a framework for computing with distributed representations that can play a role of an abstraction layer for emerging computing hardware. This article serves as a reference for computer architects by illustrating the philosophy behind VSA, techniques of distributed computing with them, and their relevance to emerging computing hardware, such as neuromorphic computing.

Junqi Tang, Mike Davies

In this work we propose an efficient stochastic plug-and-play (PnP) algorithm for imaging inverse problems. The PnP stochastic gradient descent methods have been recently proposed and shown improved performance in some imaging applications over standard deterministic PnP methods. However, current stochastic PnP methods need to frequently compute the image denoisers which can be computationally expensive. To overcome this limitation, we propose a new stochastic PnP-ADMM method which is based on introducing stochastic gradient descent inner-loops within an inexact ADMM framework. We provide the theoretical guarantee on the fixed-point convergence for our algorithm under standard assumptions. Our numerical results demonstrate the effectiveness of our approach compared with state-of-the-art PnP methods.

Julián Tachella, Junqi Tang, Mike Davies

Convolutional Neural Networks (CNNs) are now a well-established tool for solving computational imaging problems. Modern CNN-based algorithms obtain state-of-the-art performance in diverse image restoration problems. Furthermore, it has been recently shown that, despite being highly overparameterized, networks trained with a single corrupted image can still perform as well as fully trained networks. We introduce a formal link between such networks through their neural tangent kernel (NTK), and well-known non-local filtering techniques, such as non-local means or BM3D. The filtering function associated with a given network architecture can be obtained in closed form without need to train the network, being fully characterized by the random initialization of the network weights. While the NTK theory accurately predicts the filter associated with networks trained using standard gradient descent, our analysis shows that it falls short to explain the behaviour of networks trained using the popular Adam optimizer. The latter achieves a larger change of weights in hidden layers, adapting the non-local filtering function during training. We evaluate our findings via extensive image denoising experiments.

E. Paxon Frady, Garrick Orchard, David Florey et al.

Neuromorphic computing applies insights from neuroscience to uncover innovations in computing technology. In the brain, billions of interconnected neurons perform rapid computations at extremely low energy levels by leveraging properties that are foreign to conventional computing systems, such as temporal spiking codes and finely parallelized processing units integrating both memory and computation. Here, we showcase the Pohoiki Springs neuromorphic system, a mesh of 768 interconnected Loihi chips that collectively implement 100 million spiking neurons in silicon. We demonstrate a scalable approximate k-nearest neighbor (k-NN) algorithm for searching large databases that exploits neuromorphic principles. Compared to state-of-the-art conventional CPU-based implementations, we achieve superior latency, index build time, and energy efficiency when evaluated on several standard datasets containing over 1 million high-dimensional patterns. Further, the system supports adding new data points to the indexed database online in O(1) time unlike all but brute force conventional k-NN implementations.

Mohammad Golbabaee, Guido Buonincontri, Carolin Pirkl et al.

We propose a dictionary-matching-free pipeline for multi-parametric quantitative MRI image computing. Our approach has two stages based on compressed sensing reconstruction and deep learned quantitative inference. The reconstruction phase is convex and incorporates efficient spatiotemporal regularisations within an accelerated iterative shrinkage algorithm. This minimises the under-sampling (aliasing) artefacts from aggressively short scan times. The learned quantitative inference phase is purely trained on physical simulations (Bloch equations) that are flexible for producing rich training samples. We propose a deep and compact auto-encoder network with residual blocks in order to embed Bloch manifold projections through multiscale piecewise affine approximations, and to replace the nonscalable dictionary-matching baseline. Tested on a number of datasets we demonstrate effectiveness of the proposed scheme for recovering accurate and consistent quantitative information from novel and aggressively subsampled 2D/3D quantitative MRI acquisition protocols.

Junqi Tang, Karen Egiazarian, Mohammad Golbabaee et al.

In this work we investigate the practicality of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems. Such algorithms have been shown in the machine learning literature to have optimal complexities in theory, and provide great improvement empirically over the deterministic gradient methods. Surprisingly, in some tasks such as image deblurring, many of such methods fail to converge faster than the accelerated deterministic gradient methods, even in terms of epoch counts. We investigate this phenomenon and propose a theory-inspired mechanism for the practitioners to efficiently characterize whether it is beneficial for an inverse problem to be solved by stochastic optimization techniques or not. Using standard tools in numerical linear algebra, we derive conditions on the spectral structure of the inverse problem for being a suitable application of stochastic gradient methods. Particularly, we show that, for an imaging inverse problem, if and only if its Hessain matrix has a fast-decaying eigenspectrum, then the stochastic gradient methods can be more advantageous than deterministic methods for solving such a problem. Our results also provide guidance on choosing appropriately the partition minibatch schemes, showing that a good minibatch scheme typically has relatively low correlation within each of the minibatches. Finally, we propose an accelerated primal-dual SGD algorithm in order to tackle another key bottleneck of stochastic optimization which is the heavy computation of proximal operators. The proposed method has fast convergence rate in practice, and is able to efficiently handle non-smooth regularization terms which are coupled with linear operators.

Konstantinos Pitas, Andreas Loukas, Mike Davies et al.

Deep convolutional neural networks (CNNs) have been shown to be able to fit a random labeling over data while still being able to generalize well for normal labels. Describing CNN capacity through a posteriori measures of complexity has been recently proposed to tackle this apparent paradox. These complexity measures are usually validated by showing that they correlate empirically with GE; being empirically larger for networks trained on random vs normal labels. Focusing on the case of spectral complexity we investigate theoretically and empirically the insensitivity of the complexity measure to invariances relevant to CNNs, and show several limitations of spectral complexity that occur as a result. For a specific formulation of spectral complexity we show that it results in the same upper bound complexity estimates for convolutional and locally connected architectures (which don't have the same favorable invariance properties). This is contrary to common intuition and empirical results.

Konstantinos Pitas, Mike Davies, Pierre Vandergheynst

The most common method for DNN pruning is hard thresholding of network weights, followed by retraining to recover any lost accuracy. Recently developed smart pruning algorithms use the DNN response over the training set for a variety of cost functions to determine redundant network weights, leading to less accuracy degradation and possibly less retraining time. For experiments on the total pruning time (pruning time + retraining time) we show that hard thresholding followed by retraining remains the most efficient way of reducing the number of network parameters. However smart pruning algorithms still have advantages when retraining is not possible. In this context we propose a novel smart pruning algorithm based on difference of convex functions optimisation and show that it is often orders of magnitude faster than competing approaches while achieving the lowest classification accuracy degradation. Furthermore we investigate theoretically the effect of hard thresholding on DNN accuracy. We show that accuracy degradation increases with remaining network depth from the pruned layer. We also discover a link between the latent dimensionality of the training data manifold and network robustness to hard thresholding.

Mohammad Golbabaee, Zhouye Chen, Yves Wiaux et al.

Current popular methods for Magnetic Resonance Fingerprint (MRF) recovery are bottlenecked by the heavy computations of a matched-filtering step due to the growing size and complexity of the fingerprint dictionaries in multi-parametric quantitative MRI applications. We address this shortcoming by arranging dictionary atoms in the form of cover tree structures and adopt the corresponding fast approximate nearest neighbour searches to accelerate matched-filtering. For datasets belonging to smooth low-dimensional manifolds cover trees offer search complexities logarithmic in terms of data population. With this motivation we propose an iterative reconstruction algorithm, named CoverBLIP, to address large-size MRF problems where the fingerprint dictionary i.e. discrete manifold of Bloch responses, encodes several intrinsic NMR parameters. We study different forms of convergence for this algorithm and we show that provided with a notion of embedding, the inexact and non-convex iterations of CoverBLIP linearly convergence toward a near-global solution with the same order of accuracy as using exact brute-force searches. Our further examinations on both synthetic and real-world datasets and using different sampling strategies, indicates between 2 to 3 orders of magnitude reduction in total search computations. Cover trees are robust against the curse-of-dimensionality and therefore CoverBLIP provides a notion of scalability -- a consistent gain in time-accuracy performance-- for searching high-dimensional atoms which may not be easily preprocessed (i.e. for dimensionality reduction) due to the increasing degrees of non-linearities appearing in the emerging multi-parametric MRF dictionaries.

Heyi Li, Dongdong Chen, Bill Nailon et al.

We explore the use of deep learning for breast mass segmentation in mammograms. By integrating the merits of residual learning and probabilistic graphical modelling with standard U-Net, we propose a new deep network, Conditional Residual U-Net (CRU-Net), to improve the U-Net segmentation performance. Benefiting from the advantage of probabilistic graphical modelling in the pixel-level labelling, and the structure insights of a deep residual network in the feature extraction, the CRU-Net provides excellent mass segmentation performance. Evaluations based on INbreast and DDSM-BCRP datasets demonstrate that the CRU-Net achieves the best mass segmentation performance compared to the state-of-art methodologies. Moreover, neither tedious pre-processing nor post-processing techniques are not required in our algorithm.

Konstantinos Pitas, Mike Davies, Pierre Vandergheynst

Recent DNN pruning algorithms have succeeded in reducing the number of parameters in fully connected layers, often with little or no drop in classification accuracy. However, most of the existing pruning schemes either have to be applied during training or require a costly retraining procedure after pruning to regain classification accuracy. We start by proposing a cheap pruning algorithm for fully connected DNN layers based on difference of convex functions (DC) optimisation, that requires little or no retraining. We then provide a theoretical analysis for the growth in the Generalization Error (GE) of a DNN for the case of bounded perturbations to the hidden layers, of which weight pruning is a special case. Our pruning method is orders of magnitude faster than competing approaches, while our theoretical analysis sheds light to previously observed problems in DNN pruning. Experiments on commnon feedforward neural networks validate our results.

Konstantinos Pitas, Mike Davies, Pierre Vandergheynst

Recently the generalization error of deep neural networks has been analyzed through the PAC-Bayesian framework, for the case of fully connected layers. We adapt this approach to the convolutional setting.

Ping Tak Peter Tang, Tsung-Han Lin, Mike Davies

In a spiking neural network (SNN), individual neurons operate autonomously and only communicate with other neurons sparingly and asynchronously via spike signals. These characteristics render a massively parallel hardware implementation of SNN a potentially powerful computer, albeit a non von Neumann one. But can one guarantee that a SNN computer solves some important problems reliably? In this paper, we formulate a mathematical model of one SNN that can be configured for a sparse coding problem for feature extraction. With a moderate but well-defined assumption, we prove that the SNN indeed solves sparse coding. To the best of our knowledge, this is the first rigorous result of this kind.

Alhussein Fawzi, Mike Davies, Pascal Frossard

Classifiers based on sparse representations have recently been shown to provide excellent results in many visual recognition and classification tasks. However, the high cost of computing sparse representations at test time is a major obstacle that limits the applicability of these methods in large-scale problems, or in scenarios where computational power is restricted. We consider in this paper a simple yet efficient alternative to sparse coding for feature extraction. We study a classification scheme that applies the soft-thresholding nonlinear mapping in a dictionary, followed by a linear classifier. A novel supervised dictionary learning algorithm tailored for this low complexity classification architecture is proposed. The dictionary learning problem, which jointly learns the dictionary and linear classifier, is cast as a difference of convex (DC) program and solved efficiently with an iterative DC solver. We conduct experiments on several datasets, and show that our learning algorithm that leverages the structure of the classification problem outperforms generic learning procedures. Our simple classifier based on soft-thresholding also competes with the recent sparse coding classifiers, when the dictionary is learned appropriately. The adopted classification scheme further requires less computational time at the testing stage, compared to other classifiers. The proposed scheme shows the potential of the adequately trained soft-thresholding mapping for classification and paves the way towards the development of very efficient classification methods for vision problems.